Question

an electrician earns $110 after his first hour of working for a client. his total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, ... which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned? f(n + 1) = f(n) + 20 f(n + 1) = f(n) + 110 f(n + 1) = f(n + 1) + 20 f(n + 1) = f(n + 1) + 110

Explanation:

Step1: Analyze the sequence difference

The sequence is 110, 130, 150, 170, .... The difference between consecutive terms is \(130 - 110=20\), \(150 - 130 = 20\), \(170 - 150=20\).

Step2: Recall recursive - formula concept

A recursive formula for a sequence gives the next term \(f(n + 1)\) in terms of the current term \(f(n)\). In an arithmetic - sequence (where the difference between consecutive terms is constant), the general form of the recursive formula is \(f(n + 1)=f(n)+d\), where \(d\) is the common difference.

Step3: Determine the recursive formula

Since the common difference \(d = 20\), the recursive formula for the amount of money earned for each successive hour based on the amount currently earned is \(f(n + 1)=f(n)+20\).

Answer:

A. \(f(n + 1)=f(n)+20\)